Analysis of Diffusion Coefficient Distributions in Humic and Fulvic

solution to the inverse Laplace transform applied to the decay of peak intensity with gradient area in the PFG-NMR experiment. Thus, a continuous dist...
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Anal. Chem. 1999, 71, 5315-5321

Analysis of Diffusion Coefficient Distributions in Humic and Fulvic Acids by Means of Diffusion Ordered NMR Spectroscopy Kevin F. Morris,† Benjamin J. Cutak, Ann M. Dixon, and Cynthia K. Larive*

Department of Chemistry, University of Kansas, Lawrence, Kansas 66045

The use of the computer program CONTIN to analyze pulsed-field gradient NMR (PFG-NMR) data for several standard humic and fulvic acids is described. An advantage of PFG-NMR analysis is that integration of different spectral regions provides a picture of how the diffusion coefficients vary with functional group composition for a given sample. Using prior knowledge of the sample and the principle of parsimony, CONTIN approximates a solution to the inverse Laplace transform applied to the decay of peak intensity with gradient area in the PFG-NMR experiment. Thus, a continuous distribution of diffusion coefficients is resolved for the polydisperse humic and fulvic acids. The results of the CONTIN analyses are in the form of a distribution function and a two-dimensional DOSY plot. The 2D DOSY spectrum displays chemical shifts along one axis and diffusion coefficients along the other, while a number-average diffusion coefficient, DN, a weight-average diffusion coefficient, DW, and a most probable diffusion coefficient, DP, are realized from the diffusion coefficient distribution. For all spectral regions of each humic sample, DW was greater than DN, which in turn was greater than or equal to the DP, suggesting that the diffusion coefficient distribution is weighted toward smaller, more rapidly diffusing molecules. Polydispersities, estimated from the ratio DW/DN, were less than the reported MW/MN values for similar humic substances. Thus, the DW/DN ratio obtained by CONTIN analysis of PFG-NMR data can be at least a qualitative, and at best a semiquantitative, indication of the polydispersity of the humic sample, but should not be used as a quantitative measure of polydispersity. Humic substances, namely, humic acid and fulvic acid, are complex mixtures of naturally occurring organic matter. They originate from the breakdown products of terrestrial and aquatic plant and animal matter. These materials are composed of an array of both polar and nonpolar functional groups including carboxylic, phenolic, aliphatic, and aromatic groups. As a result of their various functionalities, humic substances have the ability to solubilize organic compounds as well as to complex metal cations * Corresponding author: (phone) (785) 864-4269; (fax) (785) 864-5396; (e-mail) [email protected]. † Department of Chemistry, Carthage College, Kenosha, WI 53140. 10.1021/ac9907585 CCC: $18.00 Published on Web 10/23/1999

© 1999 American Chemical Society

and, therefore, play an important role in the environmental transport and fate of anthropogenic pollutants. Given the polydisperse nature of humic substances, measurements of their properties are summations or averages of the bulk mixture.1 A number of physical and chemical measurements can be used to characterize humic substances, including titrimetry, elemental analysis, mass spectrometry, dynamic light scattering, IR spectroscopy, and 1H and 13C NMR spectroscopy.2-7 In addition to these physiochemical measurements, studies of the translational diffusion coefficients allow the overall molecular size and shape of humic compounds in the complex mixture to be characterized. Translational diffusion coefficients can also provide information regarding humic aggregation and the interaction between humic molecules and organic pollutants. Understanding these interactions will ultimately lead to a better understanding of the environmental transport and fate of such pollutants. A number of analytical techniques, including flow field-flow fractionation (FlFFF),8 dynamic light scattering (DLS),5 fluorescence correlation spectroscopy (FCS),9,10 and pulsed-field gradient NMR (PFG-NMR)11-13 can be used to measure the diffusion coefficient of a compound. Each technique has its advantages and disadvantages. For example, FlFFF requires large sample volumes and concentrations in order to obtain satisfactory data. DLS requires filtration of all samples prior to analysis in order to remove dust particles, which interfere with the scattering measurements. This filtration will undoubtedly disrupt the humic substances in solution and may adversely affect the diffusion (1) MacCarthy, P.; Rice, J. A. In Humic Substances in Soil, Sediment, and Water: Geochemistry, Isolation, and Characterization; Aiken, G. R., McKnight, D. M., Wershaw, R. L., MacCarthy, P., Eds.; John Wiley & Sons: New York, 1985; Chapter 21. (2) Ephraim, J. H.; Pettersson, C.; Morden, M.; Allard, B. Environ. Sci. Technol. 1995, 29, 622-628. (3) Petronio, B. M.; Cosma, B.; Mazzucotelli, A.; Rivaro, P. Int. J. Environ. Anal. Chem. 1993, 54, 45-56. (4) Fievre, A.; Solouki, T.; Marshall, A. G.; Cooper, W. T. Energy Fuels 1997, 11, 554-560. (5) Reid, P. M.; Wilkinson, A. E.; Tipping, E.; Jones, M. N. J. Soil Sci. 1991, 42, 259-270. (6) Santos, E. B. H.; Duarte, A. C. Water Res. 1998, 32, 597-608. (7) Malcolm, R. L. Anal. Chim. Acta 1990, 232, 19-30. (8) Dycus, P. J. M.; Healy, K. D.; Stearman, G. K.; Wells, M. J. M. Sep. Sci. Technol. 1995, 30, 1435-1453. (9) Elson, E. L.; Magde, D. Biopolymers 1974, 13, 1-27. (10) Widengren, J.; Mets, U.; Rigler, R. J. Phys. Chem. 1995, 99, 13368-13379. (11) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 1-45. (12) Price, W. S. Concepts Magn. Reson. 1997, 9, 299-336. (13) Price, W. S. Concepts Magn. Reson. 1998, 10, 197-237.

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Figure 1. One-dimensional 1H NMR spectra of the Suwannee River (a) fulvic acid and (b) humic acid.

results. Furthermore, both FlFFF and DLS are best suited for analysis of macromolecules and large molecular aggregates. These two techniques have been used to characterize higher molecular weight soil humic substances;14,15 however, many of the samples analyzed in the current work are aquatic humic substances with considerably lower molecular weights. Finally, while FCS is highly sensitive it is limited to compounds that contain fluorophores, i.e., those with aromatic moieties. On the other hand, PFG-NMR can yield diffusion coefficients for all of the 1H resonances in the NMR spectrum of a compound. However, measurements are limited to relatively concentrated solutions, because of the low sensitivity of NMR. PFG-NMR is also attractive because it can be used for mixture analysis even in regions of the spectrum where resonances from different components overlap. Because of the complexity of the humic samples, a typical humic NMR spectrum is relatively featureless compared to that of a pure compound. Figure 1 shows the broad overlapping resonances in the one-dimensional 1H NMR spectra of Suwannee River fulvic and humic acid standards. At best, only gross spectral assignments can be made,7 as summarized in Table 1. However, the PFG-NMR experiment allows for the integrated intensity of these broad spectral regions to be analyzed, yielding a diffusion coefficient for each region. This illustrates the power of the PFG-NMR technique, in that a seemingly featureless 1D spectrum can be expanded into a second dimension to provide useful molecular size information. In a PFG-NMR experiment using the bipolar pulse pair longitudinal encode-decode (BPPLED) pulse sequence,16 the intensity of a resonance, I, is related to the diffusion coefficient of the molecule, D, by eqs 1 and 2,16 where Io is the resonance

I ) Io exp[-D(∆ - δ/3 - τ/2)K2]

(1)

K ) Gγδ

(2)

intensity in the absence of a gradient pulse, ∆ is the time during (14) Pinheiro, J. P.; Mota, A. M.; d’Oliveira, J. M. R.; Martinho, J. M. G. Anal. Chim. Acta 1996, 329, 15-24. (15) Schimpf, M. E.; Petteys, M. P. Colloids Surf., A 1997, 120, 87-100. (16) Wu, D.; Chen, A.; Johnson, C. S., Jr. J. Magn. Reson. Ser. A 1995, 115, 260-264.

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which diffusion occurs, δ and G are the duration and amplitude of the bipolar magnetic field gradient, respectively, τ is the delay following each gradient pulse, and γ is the magnetogyric ratio. From these equations, it can be seen that the signals for small molecules decay more rapidly with increasing gradient strength than the signals for large molecules. Typically, a series of spectra are collected with increasing K values, and a simple linear leastsquares regression is performed to obtain D. In addition, the PFGNMR data set can be inverted to yield a two-dimensional diffusionordered spectrum (DOSY) in which 1H chemical shifts are displayed in one dimension and diffusion coefficients are displayed in the other.17-21 Previous work on fulvic acid samples has shown that, unlike single-component systems, different spectral regions can yield different diffusion coefficients.22 Therefore, a single diffusion coefficient calculated from a linear regression may not fully describe the system. Considering the fact that the humic substances are complex mixtures, it is reasonable to hypothesize that there are numerous molecules of varying shapes and sizes, which give rise to a distribution of diffusion coefficients. Thus, the objectives of this work were (1) to analyze PFG-NMR data for several standard humic materials using the computer program CONTIN to obtain diffusion coefficient distributions and 2D DOSY spectra for these samples, (2) to determine number average, DN, weight average, DW, and most probable, DP, diffusion coefficients from the distributions, and (3) to explore the use of the ratio, DW/DN, as an indication of the polydispersity of the humic substances. EXPERIMENTAL SECTION Materials. The Suwannee River humic acid reference (SRHA), fulvic acid standard (SRFA), Nordic Aquatic humic acid (NAHA), and Peat humic acid (PHA) reference samples were obtained from the International Humic Substances Society (IHSS, St. Paul, MN, June 1998). All samples were used without further purification and were prepared at a concentration of 5 mg/mL in deuterium oxide (D2O 99.9 atom % D), obtained from Cambridge Isotope Laboratories, Inc. (Andover, MA). Solutions were first acidified and lyophilized before being reconstituted in D2O, 100.0 atom % D, obtained from either Aldrich (Milwaukee, WI) or Sigma (St. Louis, MO) to reduce the overall intensity of the HOD resonance in the final spectra. Concentrated solutions of DCl and NaOD obtained from Isotec (Miamisburg, OH) and diluted in D2O were used to adjust the acidity of the SRHA, SRFA, NAHA, and PHA solutions to pD 6.5, 4.0, 6.3, and 8.0, respectively. All pH measurements were made with a Fisher Scientific Acumet 10 pH meter equipped with a 3-mm Ingold combination pH microelectrode calibrated daily with aqueous pH buffers. The pH measurements were corrected for the deuterium isotope effect, pD, by adding 0.40 to the pH meter readings.23 (17) Morris, K. F.; Johnson, C. S., Jr. J. Am. Chem. Soc. 1992, 114, 3139-3141. (18) Morris, K. F.; Johnson, C. S., Jr. J. Am. Chem. Soc. 1993, 115, 4291-4299. (19) Morris, K. F.; Stilbs, P.; Johnson, C. S., Jr. Anal. Chem. 1994, 66, 211215. (20) Chen, A.; Wu, D.; Johnson, C. S., Jr. J. Phys. Chem. 1995, 99, 828-834. (21) Jayawickrama, D. A.; Larive, C. K.; McCord, E. F.; Roe, D. C. Magn. Reson. Chem. 1998, 36, 755-760. (22) Dixon, A. M.; Larive, C. K. Anal. Chem. 1997, 69, 2122-2128. (23) Bates, R. G. Determination of pH: Theory and Practice; Wiley: New York, 1964; pp 219-220.

Table 1. Spectral Assignments7 for 1H NMR Spectra of Humic and Fulvic Acids proton chemical shift region for humic substances (ppm) region 1 0.8-1.0 0.8-1.4 1.4-1.8 region 2 1.7-3.3 region 3 3.3-5.5 region 4 6.5-8.1 8.1-9.0

types of resonances protons on terminal methyl groups of methylene chains protons on aliphatic carbons bonded to other carbons and protons on methyl groups of branched aliphatic structures protons on aliphatic carbons which are two or more carbons from an aromatic ring or polar functional group protons on carbons that are R to aromatic rings or electronegative functional groups protons on carbons directly bonded to O, N, or carbohydrates unhindered protons on aromatic rings sterically hindered protons on aromatic rings and similar structures

NMR Experiments. The diffusion coefficient measurements were carried out by performing PFG-NMR experiments using Bruker AM 360-MHz and AM 500-MHz spectrometers equipped with 5-mm actively shielded z-gradient probes. The gradient coil constants for the 360- and 500-MHz spectrometers were determined by calibration with a 10 mM β-cyclodextrin solution and were found to be 0.0531 and 0.0520 T m-1 A-1, respectively. Detailed information about the instrumentation used for the pulsed gradient measurements has been reported previously.24 All proton free induction decays (FIDs) were acquired at 298 K with a spectral width of 6024 Hz and 16 384 data points. Chemical shifts are reported relative to the HOD resonance (4.78 ppm). The PFG-NMR spectra were collected using the BPPLED pulse sequence16 with a relaxation delay of 1.2 s, a diffusion delay, ∆, of 0.10-0.20 s, a gradient pulse duration, δ, of 1.0-1.2 ms, a delay between gradient pulses, τ, of 1.1 ms, and an eddy current delay time, Te, of 15 ms. The amplitudes of the gradient pulses were varied at regular intervals from 0.027 to 0.242 T m-1 or from 0.026 to 0.515 Tm-1, depending on the spectrometer used. To achieve adequate signal-to-noise ratios in the fulvic and humic acid spectra as many as 1024 transients were coadded for each gradient. In each PFG-NMR experiment, 25-31 separate BPPLED spectra were acquired. When the resonances of two components in a mixture overlap with one another, integration of those resonances in the PFGNMR experiment yields a biexponential decay. Separate, discrete diffusion coefficients can be resolved for the two components if their diffusion coefficients differ by at least a factor of 2.17 To generalize, a spectral region with n components of n different diffusion coefficients would yield an nth-exponential decay. Given the heterogeneous nature of humic and fulvic acids, however, the mixture cannot be represented by a single or even a small number of discrete diffusion coefficients. Rather a broad, continuous distribution of diffusion rates is expected. Therefore, it is critical to analyze PFG-NMR data sets for these samples in a manner that will provide distributions of diffusion coefficients that can represent the polydisperse nature of the samples. Such an analysis was achieved by inverting the PFG-NMR data sets with the constrained regularization program CONTIN, developed by Provencher.25,26 (24) Lin, M.; Jayawickrama, D. A.; Rose, R. A.; DelViscio, J. A.; Larive, C. K. Anal. Chim. Acta 1995, 307, 449-457. (25) Provencher, S. W. Comput. Phys. Commun. 1982, 27, 213-227. (26) Provencher, S. W. Comput. Phys. Commun. 1982, 27, 229-242.

This program has been successfully applied to the analysis of diffusion coefficient distributions in polymers, phospholipid vesicles, and polymer-surfactant systems.27-29 Several alternative methods of analysis are available for the extraction of diffusion coefficients from PFG-NMR data. The list of options include using programs such as DISCRETE or SPLMOD,18 employing the CORE approach,30,31 and performing a multivariate analysis.32 The CONTIN analysis was chosen for the problem at hand because it allows a continuous distribution of diffusion coefficients to be resolved for the polydisperse humic and fulvic acid samples. CONTIN approximates a solution to the inverse Laplace transform applied to the decay of the peak intensity, I(s) with gradient area

I(s) )

∫

∞

0

G(λ) exp[-λs] ds

(3)

where λ ) (∆ - δ/3 - τ/2)D, s ) K2, and G(λ) is the diffusion coefficient distribution function. Unfortunately, the problem is illposed, and there are an infinite number of solutions that fit the data equally well. However, using prior knowledge about the nature of the problem, the user can limit the solutions only to those, physically reasonable for the system. For example, in D2O no component can diffuse faster than 5 × 10-9 m2 s-1 or slower than approximately 1 × 10-13 m2 s-1. Of the remaining solutions that are consistent with the prior knowledge, CONTIN chooses the simplest or most parsimonious solution as the best fit. As a result, narrow diffusion coefficient distributions may be somewhat oversmoothed, but by using the principle of parsimony to choose the best solution, CONTIN ensures that the distributions do not include detail not required by the data.18 One-Dimensional CONTIN Analyses. The 1H FIDs were transferred to a Silicon Graphics Indy workstation and processed using FELIX 97.0 (Biosym) Software. The FIDs were truncated at 4096 data points and apodized with 10-Hz line broadening before (27) Chen, A.; Wu, D.; Johnson, C. S., Jr. J. Am. Chem. Soc. 1995, 117, 7, 79657970. (28) Hinton, D. P.; Johnson, C. S., Jr. J. Phys. Chem. 1993, 97, 9064-9072. (29) Morris, K. F.; Johnson, C. S., Jr.; Wong, T. C. J. Phys. Chem. 1994, 98, 603-608. (30) Stilbs, P.; Paulsen, K.; Griffiths, P. C. J. Phys. Chem. 1996, 100, 81808189. (31) Stilbs, P.; Paulsen, K. Rev. Sci. Instrum. 1996, 67, 4380-4386. (32) Schulze, D.; Stilbs, P. J. Magn. Reson. Ser. A 1993, 105, 54-58.

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Fourier transformation. The line broadening parameter was chosen by trial and error of values that produced the best signalto-noise improvement with an acceptable broadening of the spectral peaks. Correction of the spectral baseline was accomplished by fitting selected baseline points to a fifth-order polynomial. A serial file of the processed spectra was then created. Spectral regions of the serial file were selected according to natural breaks in the NMR spectra as shown in Figure 1. The integrals correspond roughly to the regions defined in Table 1, except for region 3, which avoided integration of the intense HOD resonance. These regions were subsequently analyzed with CONTIN. The result of the analysis was a 50-point diffusion coefficient distribution, G(λ). DN and DW are calculated analogously to number- and weight-average molecular weights, MN and MW for polydisperse samples.33 The number-average diffusion coefficient for each distribution was calculated by dividing the first and zeroth moments of the distribution as shown in eq 4, where Gi is the

DN )

∑G D /∑G i

i

i

(4)

i

i

intensity of the distribution at the ith diffusion coefficient, Di. The maximum of the distribution was taken as the most probable diffusion coefficient, DP. Weight-average diffusion coefficients were calculated as shown in eq 5. The error in DP and DN is determined

DW )

∑ G D /∑ G D 2

i

i

i

i

i

(5)

i

by the digital resolution of the 50-point diffusion coefficient distribution. Because of propagation of error in the calculation of DW, higher errors are anticipated for this term. Two-Dimensional CONTIN Analyses. The 1H FIDs were processed as for the 1D analyses with the exception that the FIDs were truncated at 2048 data points, to build a smaller matrix. A serial file of the processed spectra was then created. A threshold intensity value was chosen by inspection of the processed file with the lowest K value. Each point above this threshold was then analyzed with CONTIN. The CONTIN analyses generated 31-point diffusion coefficient distributions, which were then interpolated to 512 points along the diffusion axis. The 2D spectra were then displayed in FELIX as contour plots. RESULTS AND DISCUSSION One-Dimensional Proton Spectra of Humic Substances. Figure 1 displays one-dimensional 1H NMR spectra of the SRHA and the SRFA. Spectral regions 1-4 corresponding to the generalized chemical shift assignments, given in Table 1, were integrated for diffusion coefficient analysis. The spectra in Figure 1 are in agreement with literature spectra for similar samples.34 Furthermore, the broad, overlapping signals clearly convey the heterogeneity of the humic substances. Diffusion Data. Examples of humic PFG-NMR data analyzed by the linear regression method are shown in Figure 2. First we (33) Mays, J. W.; Hadhjichristidis, N. In Modern Methods of Polymer Characterization; Barth, H. G., Mays, J. W., Eds.; John Wiley & Sons: New York, 1991; pp 202-204. (34) Thorn, K. A.; Folan, D. W.; MacCarthy, P. Water-Resour. Invest. (U. S. Geol. Surv.) 1989, No. 89-4196, 77-84.

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Figure 2. Echo intensity decay with magnetic field gradient strength for region 2 of (0) the Suwannee River fulvic acid and (O) the Nordic Aquatic humic acid.

note that the slope, or the diffusion coefficient, is greater for the fulvic acid than for the humic acid, (3.91 ( 0.05) × 10-10 and (3.6 ( 0.1) × 10-10 m2 s-1, respectively. Moreover, higher gradient strengths were required to produce a 95% signal attenuation with the humic acid sample. Therefore, we can conclude that the fulvic acid molecules are on average smaller and thus diffuse faster than their humic acid counterparts. This observation has also been reported by investigators utilizing other analytical techniques.35 In addition, the plots shown in Figure 2 demonstrate a pronounced deviation from linearity, especially for the humic acid sample where the correlation coefficient for the linear fit is only 0.968. Due to the fact that the deviation from linear behavior is caused by the heterogeneity of the samples, it can be concluded that the humic acid is more polydisperse than the fulvic acid. In other words, a broader distribution of diffusion rates must exist in the humic acids. This conclusion is in agreement with previous reports using other analytical methods.35 Finally, the plots in Figure 2 clearly show that all PFG-NMR data sets for humic and fulvic acids should be inverted in such a way that the polydispersity of the samples is taken into account. If instead PFG-NMR data for humic substances are analyzed by linear regression, then a significant bias in the calculated diffusion coefficients will likely result. One-Dimensional CONTIN Distributions. Given the pronounced nonexponential behavior described above, CONTIN was used to resolve one-dimensional diffusion coefficient distributions for both humic and fulvic acid samples. Representative distributions are shown in Figure 3. Note that in each case the distribution is asymmetric about the maximum, suggesting that the humic and fulvic acid samples do not contain equal concentrations of small, rapidly diffusing and larger, more slowly diffusing molecules. Thus, a most probable diffusion coefficient, DP, a numberaverage diffusion coefficient, DN, and a weight-average diffusion coefficient, DW, were calculated from the distribution function. For all spectral regions of each humic sample DW > DN g DP, again suggesting that the diffusion coefficient distribution is weighted toward smaller, more rapidly diffusing molecules. This conclusion supports observations made for similar humic substances investigated by other methods.36 (35) Beckett, R.; Jue, Z.; Gidding, J. C. Environ. Sci. Technol. 1987, 21, 289295.

Figure 3. Normalized CONTIN diffusion coefficient distributions for region 2 (a) Suwannee River fulvic acid, pD 4.0, (b) Suwannee River humic acid, pD 6.5, (c) Nordic Aquatic humic acid, pD 6.3, and (d) Peat humic acid, pD 8.0.

Figure 4. Two-dimensional DOSY spectrum of the Suwannee River fulvic acid. The narrow HOD distribution is somewhat oversmoothed by the CONTIN analysis.

Two-Dimensional CONTIN Analyses. A complimentary CONTIN analysis was also carried out to generate 2D DOSY spectra for each of the samples. A DOSY spectrum displays 1H chemical shifts along one axis and diffusion coefficients along the other, thus resolving the individual components in a complex mixture on the basis of their overall molecular size. An example DOSY spectrum for the SRFA sample is shown in Figure 4. The full 2D DOSY spectrum complements the information obtained from the one-dimensional diffusion distributions discussed previously. By performing the CONTIN analysis at each chemical shift in the 1H spectrum, subtle differences in the diffusion rate at different chemical shifts can be readily visualized. For example, the SRFA DOSY spectrum shows the resonances in proton regions 3 and 4 pulled down to slightly lower diffusion coefficient values than those of regions 1 and 2. This effect was also seen in the 1D diffusion distributions. Furthermore, since the 2D DOSY analyses allow small, rapidly diffusing species to be readily identified, it is preferable to carry out the full two-dimensional analysis before the one-dimensional (36) Lead, J. R.; Wilkinson, K. J.; Balnois, E.; Cutak, B. J.; Larive, C. K.; Assemi, S.; Beckett, R. Unpublished work; University of Geneva, Geneva, Switzerland; University of Kansas, Lawrence, KS.; and Monash University, Clayton, Victoria, Australia, 1998.

integrations. In this manner, the 2D spectrum can be closely inspected to ensure that no small-molecule impurities are present in the spectral regions to be analyzed. Integrals can then be calculated and used to generate the 1D diffusion distributions. This ability to see “at a glance” all of the different components in a complex mixture is the main advantage of the 2D DOSY analysis. Finally, we note that in the 2D spectrum the placement of the contour level threshold does distort somewhat the relative widths of the distributions at different chemical shifts. Therefore, quantitative comparisons of the distribution width for different spectral regions should be made only with the 1D CONTIN plots. Interpretation of CONTIN Results. Molecular weight determinations of humic materials also show evidence of polydispersity, and the average molecular weight measured for humic substances is governed in part by the analytical technique used. For example, methods based on measurement of colligative properties yield a number-average molecular weight, MN, which emphasizes the lower molecular weight components; while dynamic light scattering produces weight average molecular weights, MW, which emphasize the higher molecular weight species.37 Values of MN and MW for several of the humic substances examined in this work have been previously reported: SRHA, 1580 and 4390;35 SRFA, 1150 and 1910;35 and NAHA, 2272 and 3264,8 respectively. The ratio MW/MN is also a well-accepted measure of the polydispersity of the sample.33,35,38 Using an analogous argument, we examined the use of the ratio DW/DN as an indication of the polydispersity of the humic samples. As shown in Table 2, the ratio DW/DN was greater than 1 for all samples studied. This result suggests that on average the humic and fulvic samples are made up of a larger fraction of small, rapidly diffusing molecules. Although they are in relatively good agreement, the DW/DN values were less than the reported MW/MN values for similar humic substances, which ranged from 1.66 to 5.89.2,35 The lower ratios of DW/DN may reflect the lack of sensitivity of diffusion coefficients to molecular weight, scaling roughly as the cube root of the molecular weight. Furthermore, although DW and DN are conceptually similar to MW and MN, they are determined by fundamentally different measurements. Thus, the DW/DN ratio can be at least a qualitative, and at best a semiquantitative, indication of the polydispersity of the sample, but should not be used as a quantitative measure of polydispersity. There are several important trends in the data presented in Table 2. First, the SRFA DN values agree reasonably well with those reported by a linear regression analysis.22 This is expected because DN values are weighted by the faster diffusing components for this sample. The DP values, however, paint a different picture. These values tend to cluster in two groups of about 3.6 × 10-10 and 2.8 × 10-10 m2 s-1. This difference is significant and is corroborated by the 2D DOSY plot for the same sample; see Figure 4. Furthermore, all DN, DW, and DP values for the SRFA are greater than the corresponding values of the SRHA. This result is expected, because the HA fraction is normally larger with (37) Wershaw, R. L.; Aiken, G. R. In Humic Substances in Soil, Sediment, and Water: Geochemistry, Isolation, and Characterization; Aiken, G. R., McKnight, D. M., Wershaw, R. L., MacCarthy, P., Eds.; John Wiley & Sons: New York, 1985; Chapter 19. (38) Posner, A. M.; Creeth, J. M. J. Soil Sci. 1972, 23, 333-341.

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Table 2. Most Probable Diffusion Coefficients, DP, Number-Average Diffusion Coefficients, DN, Weight-Average Diffusion Coefficients, DW, and the Polydispersity Ratio, DW/DN, for Each Proton Spectral Region of the Four Humic Samples Studieda sample Suwannee River FA DP DN DW DW/DN Suwannee River HA DP DN DW DW/DN Peat HA DP DN DW DW/DN Nordic Aquatic HA DP DN DW DW/DN a

region 1

region 2

region 3

region 4

3.6 3.9 5.1 1.3

3.4 3.6 4.6 1.3

2.7 3.1 4.4 1.4

2.8 3.5 5.2 1.5

1.7 1.7 2.5 1.5

1.9 1.9 2.4 1.3

1.5 1.7 2.8 1.6

1.1 1.5 2.7 1.8

2.1 3.4 7.4 2.2

2.3 3.1 6.4 2.1

3.7 3.9 7.3 1.9

3.0 3.5 6.9 2.0

3.2 3.7 7.4 2.2

2.7 3.3 6.6 2.0

3.2 3.5 6.9 2.0

2.2 2.9 5.8 2.0

All DP and DN values are (0.2 × 10-10 m2 s-1.

respect to molecular size than the FA fraction. However, when the NAHA and PHA samples are compared to the SRFA, the DN and DP values are only slightly lower, while the DW values are greater. Three arguments can be made to explain these results. First, sample origin may be a factor. It is often difficult to generalize humic substance data from different geographical locations. In other words, fulvic acids taken from the Peat location or the Nordic location would provide a more meaningful comparison. Second, it is important to note that differences in diffusion coefficients may arise from the different solution conditions (i.e., pD) that were employed in the analysis of the various samples. Finally, the distributions of NAHA and PHA (see Figure 3) are clearly broader and more asymmetric. Thus, there is a larger fraction of components with faster diffusion rates, and consequently, a heavier weight is placed on these faster diffusion coefficients, which is magnified in the calculation of DW. Once again the results demonstrate the power and need for this new method of analysis. To assign a single diffusion coefficient, DN, to a humic sample and to use this sole value for comparisons can lead to errors. The data must be inspected holistically in terms of diffusion coefficient distributions and 2D contour maps to fully describe the sample system. The CONTIN distribution results also produced different average diffusion coefficients for each spectral region of the same humic sample. These results suggest that most humic substances are also heterogeneous with respect to chemical composition. For example, proton region 3 of SRFA produced the smallest DN, 3.1 × 10-10 m2 s-1, while proton region 1 produced the largest, 3.9 × 10-10 m2 s-1. Therefore, in this sample the fulvic molecules with a greater percentage of polar moieties are on average larger than those molecules with a greater hydrophobic character. This behavior is expected for natural organic matter, because the larger humic molecules would need a greater fraction of charged and 5320 Analytical Chemistry, Vol. 71, No. 23, December 1, 1999

polar groups to remain water soluble. Recall that differences in diffusion coefficients between spectral regions in part led to the need to analyze humic PFG-NMR data in this new manner, so these differences were not unexpected. Moreover, they actually highlight an advantage of PFG-NMR over other methods. PFGNMR can simultaneously provide diffusion coefficient information for all spectrally accessible regions. In contrast, diffusion coefficient information from FCS can only provide information about fluorophores, which essentially parallels the aromatic NMR resonances. Furthermore, diffusion coefficients measured with FCS will not be equally weighted by all aromatic molecules, because different fluorophores may have different quantum yields. While the CONTIN analysis is a robust method for analyzing PFG-NMR data for polydisperse humic and fulvic acids, the analysis does suffer from certain limitations. For example, to resolve accurate diffusion coefficient distributions, high-quality (i.e., high-S/N) data are needed. These sensitivity requirements can be met for proton experiments carried out at high magnetic fields and with concentrated samples, but they will likely be prohibitive for 13C spectroscopy. Furthermore, to adequately describe the nonexponential decay of the NMR signal with gradient strength, at least 25 different gradients must be used in each PFG-NMR experiment. This requirement can lengthen experimental time considerably. Finally, it should be noted that because the magnetization in the BPPLED experiment is transverse during the gradient encoding and decoding periods, and it is stored longitudinally during the diffusion delay, ∆, and the eddy current delay, Te, the NMR signal collected with the pulse sequence is both T1 and T2 weighted. In other words, the magnetization from very large molecules with short relaxation times may be significantly attenuated.39 Relaxation weighting has been shown to increase slightly the average diffusion coefficient measured in DOSY experiments with large phospholipid vesicles.28 However, the decay of signal intensity with gradient strength in the humic materials examined in this study indicates that no very large molecules with exceptionally short relaxation times are present in the samples. Hence, T1 and T2 weighting should be less important for the humic materials than for the much larger phospholipid vesicles. Furthermore, the relatively narrow diffusion coefficient distributions calculated for the humic and fulvic samples suggest a narrow distribution of relaxation times as well. However, T1 and T2 weighting will be a more serious concern in DOSY studies of higher molecular weight soil humic acids. In conclusion, this work has shown that, with a sufficient number of spectra and adequate signal averaging, CONTIN-DOSY analysis can be successfully applied to humic and fulvic acid samples. The asymmetry of the distributions provides information about the fraction of large and small molecules in the sample and allows for the determination the most probable diffusion coefficient, DP, and two different average diffusion coefficients, DN and DW. For all samples DW was greater than DN, which in turn was greater than or equal to DP. The ratio of the weight- and numberaveraged diffusion coefficients, DW/DN, can be used as an estimate of the polydispersity. The variation in diffusion coefficients among (39) Dixon, A. M.; Larive, C. K. Appl. Spectrosc. In press.

proton spectral regions provides information about the chemical composition of the large and small molecules. ACKNOWLEDGMENT This work was supported by a NSF-EPA Waters and Watersheds Grant, NSF CHE-9524514. The support of K.F.M. by NSF Macro-ROA Grant NSF-CHE-9321659 is gratefully acknowledged.

The 360-MHz NMR spectrometer was a generous gift of the Monsanto Co. Received for review July 12, 1999. Accepted September 13, 1999. AC9907585

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